As a promising communication paradigm, Cognitive Radio Networks (CRNs) have paved a road for Secondary Users (SUs) to opportunistically exploit unused licensed spectrum without causing unacceptable interference to Primary Users (PUs). In this paper, we study the distributed data collection problem for asynchronous CRNs, which has not been addressed before. We study the Proper Carrier-sensing Range (PCR) for SUs. By working with this PCR, an SU can successfully conduct data transmission without disturbing the activities of PUs and other SUs. Subsequently, based on the PCR, we propose an Asynchronous Distributed Data Collection (ADDC) algorithm with fairness consideration for CRNs. ADDC collects data of a snapshot to the base station in a distributed manner without any time synchronization requirement. The algorithm is scalable and more practical compared with centralized and synchronized algorithms. Through comprehensive theoretical analysis, we show that ADDC is order-optimal in terms of delay and capacity, as long as an SU has a positive probability to access the spectrum. Furthermore, we extend ADDC to the continuous data collection issue, and analyze the delay and capacity performance of ADDC in continuous data collection, which are also proven to be order-optimal. Finally, extensive simulation results indicate that ADDC can effectively finish a data collection task and significantly reduce data collection delay.